Dynamic Simulation and Model-based Control System Design for Comminution Circuits - Advanced Control and Supervision of Mineral Processing Plants - page 214

• Output variables are associated with the objective of analysis. These are usually

measurable.

• Disturbances are input variables which cannot be modified at will. These gener-

ally represent the effect of the environment on the process. These variables can
be measured in some cases.

• Parameters are variables associated with the characteristics of the system. Gen-

erally, these do not change during study.

• States are internal variables which uniquely define the behavior of the model.

A mathematical model consists of a series of mathematical relationships be-
tween these variables. These relationships can be established either through em-
pirical knowledge or by the use of first principles, such as energy and mass balance
equations. As mineral processes involve very complex phenomena, it is common to
use a combination of empirical and phenomenological models. These mathematical
relationships describe how characteristics associated with a given material flow are
transformed along the process.
The equations describing each process can be encapsulated in modules in order to
simplify programming and debugging. In addition, modules makes it easier for the
user to configure a simulation scenario, since the addition and deletion of models
does not change the simulation strategy. A simulator can then be defined as a set
of interconnected modules representing a process. Graphical interfaces of modern
simulation tools also make it possible to give the simulation diagram a look much
closer to actual engineering documents such as Process and Instrumentation (P&I)
diagrams.
If the mathematical relationships are independent of time, then the models are
static. These models serve mainly for determining operating points (through the
steady-state effect of constant manipulated variables within a time window), distur-
bances, and plant parameter changes. Although these steady-state conditions may
be arrived at using dynamic simulators, it is faster to use static simulators, which
are simpler than dynamic ones [4]. Static models have been successfully used in the
design of new plants and in the optimization of existing ones through the definition
of new operational parameters.
Dynamic models consider all time-dependent variables. In this way, it is possi-
ble to simulate transient conditions generated by changes in manipulated variables,
disturbances, different kinds of faults ( e.g. , process, instrumentation, control sys-
tem faults), plant parameter changes, etc. These types of models are very useful for
the design and verification of control systems, for on-line optimization and operator
training.